A homotopy theory for stacks
Name
49612394-MIT.pdf
Description
Full printable version
Size
4.93 MB
Format
Adobe PDF
Checksum (MD5)
2d32ca874ba96d71286bbd0855dcb976
Author(s)
Hollander, Sharon Joy, 1975-
Advisor(s)
Michael J. Hopkins.
Date Issued
2001
Publisher
Massachusetts Institute of Technology
Abstract
We give a homotopy theoretic characterization of stacks on a site C which allows one to think of stacks as the homotopy sheaves of groupoids on C. We use this characterization to construct a model category, that is a formal homotopy theory, in which stacks play the special role of the fibrant objects. This allows us to compare the different definitions of stacks and show that they lead to Quillen equivalent model categories. In addition, these model structures are Quillen equivalent to the S2-nullification of Jardine's model structure on sheaves of simplicial sets on e.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.
Includes bibliographical references (p. 69-70).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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